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There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.?
Most Upvoted Answer
There are two qunatities of oil, with the masses differing by 2 kg. Th...
Given information:
- Two quantities of oil with masses differing by 2 kg
- Same quantity of heat imparted to each mass, which is equal to 96 kcal
- Larger mass of oil was found to be 4 degrees cooler than the smaller mass
To find:
- Mass of oil in each of the two quantities
Solution:
Let the mass of the smaller quantity of oil be x kg.
Then the mass of the larger quantity of oil will be (x + 2) kg.
Let the specific heat capacity of oil be c (in kcal/kg°C).
Let the rise in temperature of the smaller quantity of oil be ΔT (in °C).
Using the formula Q = mcΔT (where Q is the quantity of heat absorbed, m is the mass, and c is the specific heat capacity), we can write:
- For the smaller quantity of oil: 96 = xcΔT
- For the larger quantity of oil: 96 = (x + 2)c(ΔT - 4)
Dividing the second equation by the first, we get:
(x + 2)/x = (ΔT - 4)/ΔT
Expanding and simplifying, we get:
xΔT + 2ΔT - 4x - 8 = xΔT
2ΔT = 4x + 8
ΔT = 2x + 4
Substituting this value of ΔT in the first equation, we get:
96 = xc(2x + 4)
24 = xc(x + 2)
Therefore, the mass of the smaller quantity of oil is x = 6 kg (using the fact that c is positive).
And the mass of the larger quantity of oil is (x + 2) = 8 kg.
Answer:
- Mass of the smaller quantity of oil is 6 kg.
- Mass of the larger quantity of oil is 8 kg.
- Two quantities of oil with masses differing by 2 kg
- Same quantity of heat imparted to each mass, which is equal to 96 kcal
- Larger mass of oil was found to be 4 degrees cooler than the smaller mass
To find:
- Mass of oil in each of the two quantities
Solution:
Let the mass of the smaller quantity of oil be x kg.
Then the mass of the larger quantity of oil will be (x + 2) kg.
Let the specific heat capacity of oil be c (in kcal/kg°C).
Let the rise in temperature of the smaller quantity of oil be ΔT (in °C).
Using the formula Q = mcΔT (where Q is the quantity of heat absorbed, m is the mass, and c is the specific heat capacity), we can write:
- For the smaller quantity of oil: 96 = xcΔT
- For the larger quantity of oil: 96 = (x + 2)c(ΔT - 4)
Dividing the second equation by the first, we get:
(x + 2)/x = (ΔT - 4)/ΔT
Expanding and simplifying, we get:
xΔT + 2ΔT - 4x - 8 = xΔT
2ΔT = 4x + 8
ΔT = 2x + 4
Substituting this value of ΔT in the first equation, we get:
96 = xc(2x + 4)
24 = xc(x + 2)
Therefore, the mass of the smaller quantity of oil is x = 6 kg (using the fact that c is positive).
And the mass of the larger quantity of oil is (x + 2) = 8 kg.
Answer:
- Mass of the smaller quantity of oil is 6 kg.
- Mass of the larger quantity of oil is 8 kg.
Community Answer
There are two qunatities of oil, with the masses differing by 2 kg. Th...
96/x - 96/x-2 = 4
put x according to option
put x according to option
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There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.?
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There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.?.
There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.?.
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There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.?, a detailed solution for There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.? has been provided alongside types of There are two qunatities of oil, with the masses differing by 2 kg. The same qunatity of heat,equal to 96 kcal, was imparted to each mass, and the larger mass of oil was found to be 4 degrees cooler than the smaller mass. Find the mass of oil in each of the two quantities.? theory, EduRev gives you an
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